Question $1-$Turing Machine computation

Consider a Turing Machine $M$ with states $Q=\{q_0,q_s,q_i,q_{ii},q_d,q_r,q_l,q_{pf},q_f,q_{zz},q_{\text{a}\text{c}\text{c}},q_{\text{r}\text{e}\text{j}}\}$ input alphabet $=\{0,1\}$ and tape alphabet $=\{0,1,,x,y,z\}.$ The transition function is given by the state diagram in the illustration below. The accept state is $q_{\text{a}\text{c}\text{c}}.$ The reject state $q_{\text{r}\text{e}\text{j}}$ is omitted from the state diagram. The start state is $q_0.$ Recall that a TM$\text{'}$s computation is deterministic. Thus, for every state qinQ and symbol $sin$ having no transition in the state diagram implicitly means that the TM enters the reject state, that is $(q,s)=(q_{\text{r}\text{e}\text{j}},s,R).$ For example, when $M$ is in state $q_{ii}$ and reads a $y,$ it would enter the reject state. If$,$ in $q_{ii}$ it reads the blank symbol $,$ then it enters the accept state.

$1$

$($a$)$ For each of the following input strings $w_i,$ trace the computation of $M$ on $w_i$ by giving the sequence of configurations that $M$ enters. For each, also state whether the input is accepted or rejected by $M.$

$w_1=010$

$w_2=100$

$w_3=1000$

$w_4=10000$

$($b$)$ Identify two more words that are accepted and two more words that are rejected by this Turing machine, all of lengths between $1$ and $10.$

$($c$)$ Provide a high$-$level description of how this Turing Machine operates and which strings are accepted and rejected.

$($d$)$ Provide pseudo$-$code $("$TM$-$algorithm"$)$ for the computation of this TM$.$ SOLVE HANDWRITTEN AND SOLVE THE QUESTION FULLY